Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting, prime radical | C23×D4×C29 | C2 |
| socle, cosocle | C23×C29 | C24 |
| hypercenter | C23×D4 | D29 |
| hypocenter | C29 | #2308 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic29 | C2 | semidirect |
| 2. #14271043 | C2 | semidirect |
| 3. #14271026 | C2 | semidirect |
| 4. #14271019 | C2 | semidirect |
| 9. C22×D4×C29 | C4 | semidirect |
| 12. C23×Dic29 | C22 | semidirect |
| 15. C2×C22⋊Dic29 | C22 | semidirect |
| 16. C2×C22⋊Dic29 | C22 | semidirect |
| 17. #11745179 | C22 | semidirect |
| 22. C24×C29 | C2×C4 | semidirect |
| 30. C2×D4×C29 | C2×C4 | semidirect |
| 32. C22×C4×C29 | C2×C4 | semidirect |
| 49. C23×C29 | C22⋊C4 | semidirect |
| 96. C22×D4 | Dic29 | semidirect |
| 105. C29 | #2308 | semidirect |
| 110. C24 | C2×Dic29 | semidirect |
| 118. C2×D4 | C2×Dic29 | semidirect |
| 123. C22×C4 | C2×Dic29 | semidirect |
| 137. C23 | C22⋊Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic29 | 2 |
| #14271043 | 2 |
| #14271026 | 2 |
| #14271019 | 2 |
| C23×D4×C29 | 2 |
| #2308 | 29 |